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<a href="_hypervolume_calculator3_d_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno">    1</span><span class="comment">/*!</span></div>
<div class="line"><a id="l00002" name="l00002"></a><span class="lineno">    2</span><span class="comment"> * </span></div>
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno">    3</span><span class="comment"> *</span></div>
<div class="line"><a id="l00004" name="l00004"></a><span class="lineno">    4</span><span class="comment"> * \brief       Implementation of the exact hypervolume calculation in 3 dimensions.</span></div>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno">    5</span><span class="comment"> *</span></div>
<div class="line"><a id="l00006" name="l00006"></a><span class="lineno">    6</span><span class="comment"> *</span></div>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno">    7</span><span class="comment"> * \author      T. Glasmachers</span></div>
<div class="line"><a id="l00008" name="l00008"></a><span class="lineno">    8</span><span class="comment"> * \date        2016-2017</span></div>
<div class="line"><a id="l00009" name="l00009"></a><span class="lineno">    9</span><span class="comment"> *</span></div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno">   10</span><span class="comment"> *</span></div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno">   11</span><span class="comment"> * \par Copyright 1995-2017 Shark Development Team</span></div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno">   12</span><span class="comment"> * </span></div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno">   13</span><span class="comment"> * &lt;BR&gt;&lt;HR&gt;</span></div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno">   14</span><span class="comment"> * This file is part of Shark.</span></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno">   15</span><span class="comment"> * &lt;https://shark-ml.github.io/Shark/&gt;</span></div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno">   16</span><span class="comment"> * </span></div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno">   17</span><span class="comment"> * Shark is free software: you can redistribute it and/or modify</span></div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno">   18</span><span class="comment"> * it under the terms of the GNU Lesser General Public License as published </span></div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno">   19</span><span class="comment"> * by the Free Software Foundation, either version 3 of the License, or</span></div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno">   20</span><span class="comment"> * (at your option) any later version.</span></div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno">   21</span><span class="comment"> * </span></div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno">   22</span><span class="comment"> * Shark is distributed in the hope that it will be useful,</span></div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno">   23</span><span class="comment"> * but WITHOUT ANY WARRANTY; without even the implied warranty of</span></div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno">   24</span><span class="comment"> * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the</span></div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno">   25</span><span class="comment"> * GNU Lesser General Public License for more details.</span></div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno">   26</span><span class="comment"> * </span></div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno">   27</span><span class="comment"> * You should have received a copy of the GNU Lesser General Public License</span></div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno">   28</span><span class="comment"> * along with Shark.  If not, see &lt;http://www.gnu.org/licenses/&gt;.</span></div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno">   29</span><span class="comment"> *</span></div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno">   30</span><span class="comment"> */</span></div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno">   31</span><span class="preprocessor">#ifndef SHARK_ALGORITHMS_DIRECTSEARCH_HYPERVOLUMECALCULATOR_3D_H</span></div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno">   32</span><span class="preprocessor">#define SHARK_ALGORITHMS_DIRECTSEARCH_HYPERVOLUMECALCULATOR_3D_H</span></div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span> </div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span><span class="preprocessor">#include &lt;<a class="code" href="_base_8h.html">shark/LinAlg/Base.h</a>&gt;</span></div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span> </div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span><span class="preprocessor">#include &lt;algorithm&gt;</span></div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span><span class="preprocessor">#include &lt;vector&gt;</span></div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span><span class="preprocessor">#include &lt;map&gt;</span></div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span> </div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceshark.html" title="AbstractMultiObjectiveOptimizer.">shark</a> {<span class="comment"></span></div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span><span class="comment">/// \brief Implementation of the exact hypervolume calculation in 3 dimensions.</span></div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span><span class="comment">///</span></div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span><span class="comment">/// M. T. M. Emmerich and C. M. Fonseca.</span></div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span><span class="comment">/// Computing hypervolume contributions in low dimensions: Asymptotically optimal algorithm and complexity results.</span></div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span><span class="comment">/// In: Evolutionary Multi-Criterion Optimization (EMO) 2011.</span></div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno">   46</span><span class="comment">/// Vol. 6576 of Lecture Notes in Computer Science, pp. 121--135, Berlin: Springer, 2011.</span></div>
<div class="foldopen" id="foldopen00047" data-start="{" data-end="};">
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"><a class="line" href="structshark_1_1_hypervolume_calculator3_d.html">   47</a></span><span class="comment"></span><span class="keyword">struct </span><a class="code hl_struct" href="structshark_1_1_hypervolume_calculator3_d.html" title="Implementation of the exact hypervolume calculation in 3 dimensions.">HypervolumeCalculator3D</a> {<span class="comment"></span></div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno">   48</span><span class="comment">    /// \brief Executes the algorithm.</span></div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span><span class="comment">    /// \param [in] points The set of points for which to compute the volume</span></div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span><span class="comment">    /// \param [in] refPoint The reference point \f$\vec{r} \in \mathbb{R}^3\f$ for the hypervolume calculation, needs to fulfill: \f$ \forall s \in S: s \preceq \vec{r}\f$.</span></div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span><span class="comment"></span>    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> Set, <span class="keyword">typename</span> VectorType &gt;</div>
<div class="foldopen" id="foldopen00052" data-start="{" data-end="}">
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"><a class="line" href="structshark_1_1_hypervolume_calculator3_d.html#a5380fba06eafd3dcd3891e8998a61882">   52</a></span>    <span class="keywordtype">double</span> <a class="code hl_function" href="structshark_1_1_hypervolume_calculator3_d.html#a5380fba06eafd3dcd3891e8998a61882" title="Executes the algorithm.">operator()</a>( Set <span class="keyword">const</span>&amp; points, <a class="code hl_typedef" href="_c_svm_linear_8cpp.html#ab106d665148183a2dc94dcf8716c9203">VectorType</a> <span class="keyword">const</span>&amp; refPoint){</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno">   53</span>        <span class="keywordflow">if</span> (points.empty()) <span class="keywordflow">return</span> 0.0;</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno">   54</span>        <a class="code hl_define" href="_exception_8h.html#a42a6a50e4d06c00d60fbca5333f40768">SIZE_CHECK</a>(points.begin()-&gt;size() == 3);</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno">   55</span>        <a class="code hl_define" href="_exception_8h.html#a42a6a50e4d06c00d60fbca5333f40768">SIZE_CHECK</a>(refPoint.size() == 3);</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno">   56</span> </div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno">   57</span>        std::vector&lt;VectorType&gt; set;</div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno">   58</span>        <span class="keywordflow">for</span> (std::size_t i=0; i&lt;points.size(); i++)</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno">   59</span>        {</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>            <a class="code hl_typedef" href="_c_svm_linear_8cpp.html#ab106d665148183a2dc94dcf8716c9203">VectorType</a> <span class="keyword">const</span>&amp; p = points[i];</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>            <span class="keywordflow">if</span> (p[0] &lt; refPoint[0] &amp;&amp; p[1] &lt; refPoint[1] &amp;&amp; p[2] &lt; refPoint[2]) set.push_back(p);</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>        }</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>        <span class="keywordflow">if</span> (set.empty()) <span class="keywordflow">return</span> 0.0;</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>        std::sort(set.begin(), set.end(),</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span>                    [] (<a class="code hl_typedef" href="_c_svm_linear_8cpp.html#ab106d665148183a2dc94dcf8716c9203">VectorType</a> <span class="keyword">const</span>&amp; x, <a class="code hl_typedef" href="_c_svm_linear_8cpp.html#ab106d665148183a2dc94dcf8716c9203">VectorType</a> <span class="keyword">const</span>&amp; y)</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>                    { return (x[2] &lt; y[2]); }</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>                );</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno">   68</span> </div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno">   69</span>        <span class="comment">// add the first point</span></div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno">   70</span>        std::map&lt;double, double&gt; front2D;</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno">   71</span>        <a class="code hl_typedef" href="_c_svm_linear_8cpp.html#ab106d665148183a2dc94dcf8716c9203">VectorType</a> <span class="keyword">const</span>&amp; x0 = set[0];</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno">   72</span>        front2D[x0[0]] = x0[1];</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno">   73</span>        <span class="keywordtype">double</span> prev_x2 = x0[2];</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno">   74</span>        <span class="keywordtype">double</span> area = (refPoint[0] - x0[0]) * (refPoint[1] - x0[1]);</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno">   75</span>        <span class="keywordtype">double</span> volume = 0.0;</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span> </div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>        <span class="comment">// process further points</span></div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>        <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i=1; i&lt;set.size(); i++)</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>        {</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>            assert(! front2D.empty());</div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>            assert(area &gt; 0.0);</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span> </div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>            <a class="code hl_typedef" href="_c_svm_linear_8cpp.html#ab106d665148183a2dc94dcf8716c9203">VectorType</a> <span class="keyword">const</span>&amp; x = set[i];</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span> </div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>            <span class="comment">// check whether x is dominated and find &quot;top&quot; coordinate</span></div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>            <span class="keywordtype">double</span> t = refPoint[1];</div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno">   87</span>            std::map&lt;double, double&gt;::iterator right = front2D.lower_bound(x[0]);</div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno">   88</span>            std::map&lt;double, double&gt;::iterator left = right;</div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno">   89</span>            <span class="keywordflow">if</span> (right == front2D.end())</div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span>            {</div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>                --left;</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>                t = left-&gt;second;</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno">   93</span>            }</div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno">   94</span>            <span class="keywordflow">else</span></div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno">   95</span>            {</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno">   96</span>                <span class="keywordflow">if</span> (right-&gt;first == x[0])</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno">   97</span>                {</div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno">   98</span>                    t = left-&gt;second;</div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>                }</div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>                <span class="keywordflow">else</span> <span class="keywordflow">if</span> (left != front2D.begin())</div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span>                {</div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>                    --left;</div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>                    t = left-&gt;second;</div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span>                }</div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>            }</div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>            <span class="keywordflow">if</span> (x[1] &gt;= t) <span class="keywordflow">continue</span>;   <span class="comment">// x is dominated</span></div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span> </div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span>            <span class="comment">// add chunk to volume</span></div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>            volume += area * (x[2] - prev_x2);</div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span> </div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span>            <span class="comment">// remove dominated points and corresponding areas</span></div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>            <span class="keywordflow">while</span> (right != front2D.end() &amp;&amp; right-&gt;second &gt;= x[1])</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>            {</div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span>                std::map&lt;double, double&gt;::iterator tmp = right;</div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>                ++right;</div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>                <span class="keyword">const</span> <span class="keywordtype">double</span> r = (right == front2D.end()) ? refPoint[0] : right-&gt;first;</div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span>                area -= (r - tmp-&gt;first) * (t - tmp-&gt;second);</div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>                front2D.erase(tmp);</div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>            }</div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span> </div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>            <span class="comment">// add the new point</span></div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span>            <span class="keyword">const</span> <span class="keywordtype">double</span> r = (right == front2D.end()) ? refPoint[0] : right-&gt;first;</div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>            area += (r - x[0]) * (t - x[1]);</div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>            front2D[x[0]] = x[1];</div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno">  125</span> </div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno">  126</span>            <span class="comment">// volume is processed up to here:</span></div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno">  127</span>            prev_x2 = x[2];</div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno">  128</span>        }</div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno">  129</span> </div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno">  130</span>        <span class="comment">// add trailing chunk to volume</span></div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno">  131</span>        volume += area * (refPoint[2] - prev_x2);</div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span> </div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>        <span class="comment">// return the result</span></div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>        <span class="keywordflow">return</span> volume;</div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>    }</div>
</div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>};</div>
</div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span> </div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno">  138</span>}</div>
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno">  139</span><span class="preprocessor">#endif</span></div>
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